Norm along side axis

[DPDmancul]

It would be nice if the LinearAlgebra.norm function have the dims keyword, like others linear algebra functions and like numpy norm axis parameter (https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.norm.html)

Just for example:

function norm(itr, p::Real=2; dims)
    sum(itr.^p; dims=dims).^(1/p)
end

[andreasnoack]

I think we are generally moving towards delegating these kinds of computations to mapslices or https://github.com/bramtayl/JuliennedArrays.jl

[dkarrasch]

Ignoring the "wrong" orientation of the resulting array, doing it via eachslice seems way faster:

using LinearAlgebra, BenchmarkTools
A = rand(100, 100);
@btime map(norm, eachslice($A, dims=2));  #  5.689 μs (105 allocations: 5.64 KiB)
@btime mapslices(norm, $A, dims=1);  #  61.642 μs (838 allocations: 24.02 KiB)

(The two compute the same despite the different dims, see JuliaLang/julia#34840.)

[mcabbott]

The eachslice version is still a lot slower than working on one big array:

function norm2(A; dims)
    B = sum(x -> x^2, A; dims=dims)
    B .= sqrt.(B)
end
@btime norm2($A, dims=1); # 1.786 μs (1 allocation: 896 bytes)

Even if calling map(norm, eachslice) ends up being the preferred interface, it seems worthwhile to have some implementation like this.